pdf file

Nuclear
Nuclear
Physics
Physics
from
on Lattice
the lattice
QCD
particle physics
nuclear physics
astrophysics
1 fm
10 fm
10 km
Tetsuo Hatsuda (Univ. Tokyo)
RIKEN Lattice WS, Sep.26, 2010
計算科学と密接に関係する挑戦的課題
--- 我々はどこから来てどこへ行くのか？ --⇔ LHC
・ 物質の究極構造
-- 超弦理論、真空の構造、精密QCD
・ 宇宙初期の極限物質
⇔ RHIC, LHC
-- 超高温状態（1012 K）とビッグバン
・ 重元素の起源
⇔ RIBF
-- 鉄より重い元素はどのように生まれたのか？
・ 星の終焉での極限物質
⇔ J-PARC
-- 超高密度状態（1012 kg/cm3）と
中性子星、クォーク星、ブラックホール
LATTICE QCD inputs are crucial
京速シンポ (2006年4月)
T. Hatsuda, Keisoku-symp.
(April 5, 2006)
T. Hatsuda, Keisoku-symp.
(April 5, 2006)
T. Hatsuda, Keisoku-symp.
(April 5, 2006)
1 fm
10 fm
Outline
[1] nuclear force – nuclei and neutron stars
[2] nuclear force from lattice QCD
[3] hyperon force – hyperonic matter and neutron star core
[4] Hyperon force from lattice QCD
[5] origin of repulsive core and the Pauli principle
[6] Summary and Future
10 km
2D (N-Z) Nuclear Chart
(Segrè)
~300
~3000
> 7000
ab initio nuclear A-body calculations (2001-)
A≦ 5
H, |ψ〉
A ≦ 12
H, |ψ〉
A ≦ 56
Heff, |ψeff〉
UMOA, UCOM,
SRG, …
・Faddeev
H, |ψ〉
・ diaginalization
・Green’s function Monte Carlo
・diagonalization after reduction
(coupled cluster, NCSM, NC-MCSM, …)
Benchmark Calculations of 4He by 7 methods  agreement within 0.5%
Phys. Rev. C64, 044001 (2001) [arXiv:nucl-th/0104057].
Example: Green’s Function Monte Carlo for light nuclei
NN scattering Phenomenological
data
inputs
n = (a few) x 100
4He
S.C.Pieper, ``Quantum Monte Carlo Calculations of Light Nuclei,''
Riv. Nuovo Cim. 031, 709 (2008) [arXiv:0711.1500 [nucl-th]].
8Be
NN
+NNN
S.C.Pieper, Riv. Nuovo Cim. 031, 709 (2008)
[arXiv:0711.1500 [nucl-th]].
NN interactions
critical inputs in nuclear physics
virtual state
mid-range
attraction
short-range
repulsion
2S+1
LJ
deuteron
mid-range
attraction
short-range
repulsion
Nijmegen partial-wave analysis,
Stoks et al., Phys.Rev. C48 (1993) 792
Key features of the Nuclear force
 One-pion exchange
Yukawa (1935)
 Multi-pions
Taketani et al.
(1951)
 Repulsive core
Jastrow (1951)
repulsive
core
2π, 3π, ...
π
 EFT for NN int.
Weinberg (1990)
Modern high precision
NN forces (90’s-)
phenomenological NN interactions
-- how many parameters ? -R. Machleidt, arXiv:0704.0807 [nucl-th]
~ 4500 np and pp scattering data (Tlab < 300 MeV)
NNN, YN, YY: data very limited
phenomenological NN interactions
-- how many parameters ? -R. Machleidt, arXiv:0704.0807 [nucl-th]
high precision
NN interactions
CD Bonn
(p space)
AV18
(r space)
EFT in N3LO (nπ+contact)
# of
parameters
38
40
24
χ2/dof
~1
~1
~ (1-2)
~ 4500 np and pp scattering data (Tlab < 300 MeV)
NNN, YN, YY: data very limited
Nuclear Force and Neutron Star
(ρmax
～
6ρ0)
PSR1913+16
Neutron star binary
Pressure balance
Fermi pressure
Repulsive core
gravity
Nuclear Force and Neutron Star
(ρmax
～
6ρ0)
PSR1913+16
Neutron star binary
Oppenheimer-Volkov(1939)
Pressure balance
Fermi pressure
Repulsive core
gravity
Nuclear Force and Neutron Star
(ρmax
NNN
～
6ρ0)
PSR1913+16
NN
Neutron star binary
Pressure balance
Fermi pressure
Repulsive core
gravity
1 fm
10 fm
Outline
[1] nuclear force – nuclei and neutron stars
[2] nuclear force from lattice QCD
[3] hyperon force – hyperonic matter and neutron star core
[4] Hyperon force from lattice QCD
[5] origin of repulsive core and the Pauli principle
[6] Summary and Future
10 km
Nuclear Physics from QCD
1. Lattice scattering length
Kuramashi et al. (1995)
Ishizuka with CP-PACS Coll. (2005)
NPLQCD Coll. (2006-)
2. Lattice potential
Aoki, Hatsuda, Ishii (2006) + Nemura (2007)
HAL QCD Coll. (2009-)
3. Lattice nuclei
Yamazaki, Kuramashi, Ukawa (2009)
4. Strong coupling nuclei
Ohnishi et al.(2007-) de Forcrand et al. (2009)
5. Holographic nuclei
Hashimoto et al. (2009-)
Nuclear Physics from QCD
Ask HAL !
1. Lattice scattering length
Kuramashi et al. (1995)
Ishizuka with CP-PACS Coll. (2005)
NPLQCD Coll. (2006-)
2. Lattice potential
Aoki, Hatsuda, Ishii (2006) + Nemura (2007)
HAL QCD Coll. (2009-)
3. Lattice nuclei
Yamazaki, Kuramashi, Ukawa (2009)
4. Strong coupling nuclei
Ohnishi et al.(2007-) de Forcrand
et T.
al.Hatsuda
(2009) (Tokyo)
N. Ishii,
5. Holographic nuclei
Hashimoto et al. (2009-)
T. Doi, K. Sasaki, S. Aoki (Tsukuba)
K. Murano (KEK), T. Inoue (Nihon)
Y. Ikeda (RIKEN), H. Nemura (Tohoku)
N. Ishii, T. Hatsuda (Tokyo)
T. Doi, K. Sasaki, S. Aoki (Tsukuba)
K. Murano (KEK), T. Inoue (Nihon)
Y. Ikeda (RIKEN), H. Nemura (Tohoku)
Imaginary time
x
J
y
space
y
Lüscher’s Method :
HAL QCD Method :
J
+ all possible
combinations
y
φ(r > R)  phase shifts :
φ(r < R)  non-local potentials
 observables, many-body systems :
Lattice NN potential
Lüscher’s Method : φ(r > R)  phase shifts
HAL QCD Method : φ(r < R)  non-local potentials
 observables, many-body systems
Quenched QCD (mπ=530MeV, L=4.4 fm)
(2+1)-flavor QCD (mπ=570MeV, L=2.9 fm)
r [fm]
Ishii, Aoki, Hatsuda, PRL 99 (2007) 022001
Ishii, Aoki, Hatsuda, arXive 0903.5497 [hep-lat]
HAL QCD procedure : 5 steps to go
Aoki, Hatsuda & Ishii,
PTP 123 (2010) 89-128
[0909.5585 [hep-lat]],
(i) Choose a composite operator: e.g.
(ii) Measure the BS amplitude:
(iii) Calculate off-shell T-matrix:
(iv) Derive non-local potential:
(v) Make derivative expansion:
LO
LO
NLO
NNLO
Key channels in NN scattering (2s+1LJ)
LO
1S
0
Central force
LO
NLO
NNLO
nuclear BCS pairing
Bohr, Mottelson & Pines, Phys. Rev. 110 (1958)
3S -3D
1
1
Tensor force
deuteron binding
Pandharipande et al., Phys. Rev. C54 (1996)
3 P - 3F
2
2
LS force
neutron superfluidity
in neutron stars
Tamagaki, Prog. Theor. Phys. 44 (1970)
Density profile
of the deuteron
with Sz=±1
LO potentials : VC(r) & VT(r)
mixing between 3S1 and 3D1 through the tensor force
LO potentials : VC(r) & VT(r)
quenched QCD
E ～ 0 MeV
Aoki, Hatsuda & Ishii,
0909.5585 [hep-lat]
PTP 123 (2010) 89-128
Aoki, Hatsuda & Ishii,
0909.5585 [hep-lat]
PTP 123 (2010) 89-128
LO potentials : VC(r) & VT(r)
VT(r)
VC(r)
quenched QCD
quenched
E ～QCD
0 MeV
E ～ 0 MeV
Vc(r0) ~ (log r)β/r2, VT(r0) 0 from OPE
Aoki, Balog & Weisz, JHEP 1005, 008 (2010)
Aoki, Hatsuda & Ishii,
0909.5585 [hep-lat]
PTP 123 (2010) 89-128
LO potentials : VC(r) & VT(r)
VT(r)
VC(r)
quenched QCD
quenched
E ～QCD
0 MeV
E ～ 0 MeV
quenched QCD
E ～ 0 MeV
fit function
・Rapid
dependence of VT(r)
・Rapid quark-mass dependence
of quark-mass
VT~(r)
Vc(r0)
(log r)β/r2, VT(r0) 0 from
OPE
・Evidence
of
the
one-pion-exchange
・Evidence of the one-pion-exchange
Aoki, Balog & Weisz, JHEP 1005, 008 (2010)
NNLO potential of O(∇2): how large ?
●
PBC
(TLab～0 MeV)
●
APBC (TLab～100 MeV)
Murano [Parallel 38, Thur.]
NNLO potential of O(∇2): how large ?
●
PBC
(TLab～0 MeV)
●
APBC (TLab～100 MeV)
Murano [Parallel 38, Thur.]
NNLO potential of O(∇2): how large ?
●
PBC
(TLab～0 MeV)
●
APBC (TLab～100 MeV)
1S
0
Murano [Parallel 38, Thur.]
NN phase shifts in (2+1)-flavor QCD
3S
1
VCeff(r)
3S phase
1
shift from VCeff(r)
3S phase
1
deuteron not bound
for mπ ≧410 MeV
Ishii et al. (HAL QCD Coll.),
arXiv:1004.0405 [hep-lat]
3S
1
shift (exp.)
“Feshbach resonances” in hadrons and ultracold atoms
Kuramashi [hep-lat/9510025]
a0 [fm]
N-N
40K-40K
3S
1
1S
0
1S
0
Regal & Jin, PRL 90, 230404 (2003)
3S
1
[MeV]
Discovery of BEC-BCS crossover
“Feshbach resonances” in hadrons and ultracold atoms
Kuramashi [hep-lat/9510025]
a0 [fm]
N-N
40K-40K
unitary regime
3S
1
1S
0
1S
0
Regal & Jin, PRL 90, 230404 (2003)
3S
1
[MeV]
NN interaction
・net attraction at low energy
・still far from “unitary regime”
・ V(r) : mild func. of mq
a0 : highly sensitive to mq
Discovery of BEC-BCS crossover
 UMOA (Fujii, Okamoto, Suzuki), PRL103, 182501 (2009)
基底状態エネルギー（2体核力: CD Bonn）
56Ni(97.8%), 40Ca(99.5%), 16O(93.6%) カッコ内は、計算結果/実験値
• 良く実験値を再現するが、2体核力の違いによって計算結果にばらつきがある。
（Nijm Iの場合、40Ca(88.3%)）
• 2体力と理論的に整合性のとれた3体力などの多体力の必要性。
（現象論的パラメータを多く含む現象論的核力ではその構築は困難）
現在・・・カイラル摂動理論に基づく2体力と整合性のとれた3体力(および4体力）
の構築が世界各地で進行中。
今後・・・格子QCD計算に基づく2体力、3体力などの統一的な構築の重要性大。
adapted from S. Fujii
1 fm
10 fm
Outline
[1] nuclear force – nuclei and neutron stars
[2] nuclear force from lattice QCD
[3] hyperon force – hyperonic matter and neutron star core
[4] Hyperon force from lattice QCD
[5] origin of repulsive core and the Pauli principle
[6] Summary and Future
10 km
YN and YY interactions
Radius ～ 10 km
Mass ～ solar mass
Central density ～ 1012 kg/cm3
Hyperon matter?
Solid
Crust
Neutron
Liquid
YN and YY interactions
Radius ～ 10 km
Mass ～ solar mass
Central density ～ 1012 kg/cm3
Hyperon matter?
Solid
Crust
Schaffner-Bielich, ``Strangeness in Compact Stars,''
Nucl. Phys.A 835, 279 (2010) [arXiv:1002.1658 [nucl-th]].
Neutron
Liquid
M-R relation of Neutron Stars and dense EOS
Thermonuclear Burst in X-ray Binaries
4U 1608-248 EXO 1745-248 4U 1820-30
(i) Apparent surface area
R 2  2GM 
A = 2 4 1 −

D fc 
R 
−1
(ii) Eddington limit
4πGM  2GM 
1−
=

2 
κ cs D 
R 
1/ 2
Fedd
Ozel, Baym & Guver, arXiv: 1002.3153 [astro-ph.HE]
(N-Z) Nuclear
3D2D
(N-Z-S)
nuclearChart
chart
J-PARC@KEK, Japan（2009-）
3 known
40 known
~3000 known
Λ hypernuclei
Λ
UΛ = - 30 MeV
(UN = - 50 MeV)
Hotchi et al., PRC 64 (2001) 044302
A. Umeya. J-PARC Hadron Salon talk
(Aug.11, 2010)
double-Λ hypernuclei
Λ
Λ
4He+Λ+Λ
7.25 ±0.1 MeV
0+
・ ΛN attraction
・ ΛΛ weak attraction
・ No deeply bound H-dibaryon
1 fm
10 fm
Outline
[1] nuclear force – nuclei and neutron stars
[2] nuclear force from lattice QCD
[3] hyperon force – hyperonic matter and neutron star core
[4] Hyperon force from lattice QCD
[5] origin of repulsive core and the Pauli principle
[6] Summary and Future
10 km
ΛN interaction in (2+1)-flavor QCD
LO potentials from BS wave function
(2+1)-flavor, Iwasaki + clover (PACS-CS)
L=2.9fm, a=0.09fm, 323x64
Nemura et al. (HAL QCD Coll.)
arXiv: 1005.5352 [hep-lat]
Scattering length
from Lüscher’s formula
with k from BS wave function
LO potentiald
from BS wave function
ΛN interaction
・repulsive core + attractive well
・net attraction at low energy
精密ハイパー核計算によるハイペロン力 の選別
13C
Λ
炭素のハイパー同位体
Λ
4He
ハイペロン力以外の不定性を
精密計算（無限小ガウスローブ法）で排除
精密計算の予言
3/2-
960
keV
～
360
ハイペロン力
（中間子交換模型)
1/23/2-
4He
後の実験結果(BNL-E929)
150
～
1/2-
4He
200
keV
1/23/2-
152
± 54
± 36
keV
ハイペロン力
(クォーク模型)
肥山詠美子氏（理研）提供
1 fm
10 fm
Outline
[1] nuclear force – nuclei and neutron stars
[2] nuclear force from lattice QCD
[3] hyperon force – hyperonic matter and neutron star core
[4] Hyperon force from lattice QCD
[5] origin of repulsive core and the Pauli principle
[6] Summary and Future
10 km
BB interactions
in a SU(3) symmetric world
x
1. First step to predict YN, YY interactions not accessible in exp.
2. Origin of the repulsive core (universal or not)
Six independent potentials in flavor-basis
M. Oka. J-PARC Hadron Salon talk
(June.17, 2010)
Equal-time BS amplitudes in the SU(3) limit
1
27
Iwasaki + clover (CP-PACS/JLQCD)
Ｌ=1.9 fm, a=0.12 fm, 163x32
mπ=835 MeV, mB=1752 MeV
Inoue et al. (HAL QCD Coll.)
ArXiv:1007.3559 [hep-lat]
PTP (2010) in press.
8s
Pauli principle at work !
1 : allowed
27 : partially blocked
8s : almost blocked
c.f. Oka, Shimizu, Yazaki ,
Nucl. Phys. A464 (1987) 700
BB potentials in flavor-basis (1S0 channel)
NN
BB potentials in flavor-basis (1S0 channel)
NN
BB potentials in flavor-basis (1S0 channel)
NN
mπ=749 MeV, mπ/mK=0.904
K. Sasaki (HAL QCD)
S-wave ηc-N interaction
cc
no Pauli-blocking + QCD van der Walls attraction
 charmonium-nucleus bound state ?
Brodsky et al., PRL 64 (1990) 1011
Quenched QCD: 323x48, L = 3 fm
(2+1)-flavor QCD on-going
BS wave function
Kawanai & Sasaki, ArXiv:1009.3332 [hep-lat]
Potential
S-wave K+-p interaction
Iwasaki + Clover (CP-PACS/JLQCD)
a= 0.12 fm, L=1.9 fm, 163x32
mπ = 871 MeV, mK = 912 MeV
mN = 1796 MeV
Ikeda et al. (HALQCD Coll.)
us
ミクロ（素粒子・ハドロン・原子核）からマクロ（宇宙）への架け橋が
今後５年間に国内で大きく進展する？
素粒子
RIBF (2007-)
ハドロン・原子核
J-PARC (2009-)
宇宙
次世代スパコン (2012-)
Lattice Potentials
Lattice Nuclei
+ ab initio Nuclear Calculation
Imaginary Nuclei (mq > mqphys)
Ordinary Nuclei
Strange & Charm Nuclei
Holographic Nuclei
三層構造の重要性
文科省「特定先端大型研究施設の
共用の促進に関する基本的方針」
に対する意見
2008年3月20日
素粒子論グループ
１０ Eflops
スパコンセンター
１ Eflops
KEK, RIKEN,
YITP, RCNP, ..
Ｘ １０００
各研究室のクラスター
１０ Pflops
２０２５年
スパコンセンター
１ Pflops
KEK, RIKEN,
YITP, RCNP, ..
各研究室のクラスター
２０１２年
Ｘ １０００
第一層： 挑戦的課題
第二層： 中小規模プロジェクト
第三層： 萌芽的課題